find the codomain of f(x) = (x+3) / (x-1)

The equation is written as

Aisha has 15 points

Let's use the given information to set up an equation to represent the relationship between the points each friend has.

Let x be the number of points Aisha has.

Then, according to the problem statement, we know that:

Carter has 7 1/2 more points than Aisha, so he has

x + 7 1/2 points.

Jamila has 4 - 1/2 more points than Carter, so she has

x + 7 1/2 + 4 - 1/2 points,

which simplifies to x + 11 points.

Jamila has 26 points, so we can set x + 11 equal to 26 and solve for x:

x + 11 = 26

x = 26 - 11

x = 15

Therefore, Aisha has 15 points.

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Answer:

Step-by-step explanation:

and

we are done

The equation of a circle is a measure of its center and its radius.

The equation of the circle is: \(x^2 + y^2 - 14x -8y + 56 = 0\)

The general equation of a circle is \((x - a)^2 + (y - b)^2 + r^2\). Where:

\((a,b) \to\) center

\(r \to\) radius

From the given figure, we have:

\(r = 3\)

\((a,b) = (7,4)\)

So, the equation of the circle is:

\((x - a)^2 + (y - b)^2 + r^2\)

\((x - 7)^2 + (y - 4)^2 = 3^2\)

\((x - 7)^2 + (y - 4)^2 = 9\)

Open brackets

\(x^2 - 14x + 49 + y^2 -8y + 16 = 9\)

Collect like terms

\(x^2 + y^2 - 14x -8y + 49 + 16 - 9 = 0\)

\(x^2 + y^2 - 14x -8y + 56 = 0\)

Hence, the equation of the given circle is: \(x^2 + y^2 - 14x -8y + 56 = 0\)

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Answer:

m=-3/2

b=3

equation f(x) = -3/2x +3

Proportional

negative slope

Step-by-step explanation:

Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

Answer:

False

Step-by-step explanation:

We have several terms that we can take reference to in this true or false situation. The first is Central Tendency which measures for locating a single score that's most representative or descriptive of all scores in a distribution.

Given text:

The sum of the squared differences of scores from their mean is zero.

The main term within this sentence is the word mean. This term is the sum of a set divided by the total (#) of scores summed.

In order to determine whether this is true or false, we must list what is referred to as the 5 characteristics of the term Mean.

1. Changing an existing score will change the mean.

2.Adding a new score or removing an existing score will change the mean, unless that value equals the mean.

3. Adding, subtracting, multiplying, or dividing each score in a distribution by a constant will cause the mean to change by that constant.

4. The sum of the differences of scores from their mean is zero.

5. The sum of the squared differences of scores from their mean is minimal.

After taking closer analysis, there has been clarification within the characteristics of the mean confirming that the answer is indeed false.

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Answer:

0.75

Step-by-step explanation:

it makes sense that 3 is the Dividend, 4 is the Divisor, and you want to know the Quotient. Thus, the answer is:

3 ÷ 4 = 0.75

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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Answer:

Sean is late for dinner.

Step-by-step explanation:

A quarter to 7 is 6:45 so he is 15 minutes late to the dinner.

If Sean arrives at quarter to 7 (which means 6:45), he is 15 minutes late for dinner, as dinner started at 6:30.

When we say that Sean arrived at quarter to 7, it means that he arrived at 6:45, because a quarter of an hour is equivalent to 15 minutes. We can then compare this time to the time that dinner started, which is 6:30.

If Sean arrived at or before 6:30, he would be considered early for dinner. However, since he arrived at 6:45, he is 15 minutes late for dinner. This means that dinner has already started and he has missed the beginning of the meal.

In general, it is considered polite and respectful to arrive on time for a dinner invitation or any other social event. If you are going to be late, it's always a good idea to let your host know so they can adjust their plans accordingly.

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Answer:

To calculate the gradient of a straight line we choose two points on the line itself. From these two points we calculate: The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates). If the answer is a positive value then the line is uphill in direction.

Answer:

(x-4)(3x+2)

Step-by-step explanation:

Answer:

\((3x+2)(x-4)\)

Step-by-step explanation:

Something to keep in mind is that the factored expression will be in either the form of \((ax-b)(x-c)\) or \((ax-b)(cx-d)\). In either case, the final term will only be the product of -b and -c in the first case or -b and -d in the second case. This means that the term without an x will not be affected by the coefficient of x.

We have the following expression

\(3x^2-10x-8\)

The first thing we can do is list out the factors of -8

1 and -8

-1 and 8

2 and -4

-2 and 4

These are all of the pairs that could be factors of -8.

Normally, the next step would be to look for which of these factors would add together to give you the coefficient of x, but as there is a 3\(x^2\), this is complicated a little more.

Instead, we have to look for 3 multiplied by one of the factors and then added to the other factor. In the case of this problem, the result must be -10.

At this point, you just have to begin testing out which ones will work.

Let us look at the factors 2 and -4

\(2(3)-4=2\\\\2-4(3)=-10\)

We can see that while the first one didn't work, the second one resulted in -10, which is what we wanted.

Now that we know what the factors are, let us write them in the form\((ax-b)(x-c)\)

Normally, it does matter which number you pair with each x, but in this case, it does matter. As we had to multiply the -4 by 3, it must be in the pair that is opposite to the pair with the 3x.

Knowing this, we can construct out factor

\((3x+2)(x-4)\)

(Sorry that this explanation was quite lengthy)

The derivatives of the functions are now listed:

19) f'(x) = 3

23) f'(x) = 2 · x - 6 · x²

25) g'(x) = - 1 / [2 ·√(9 - x)]

27) g'(t) = - 2 / 3

In this case we have four functions, whose first derivatives must be found by means of derivative rule. Now we present the result of each expression along with the corresponding derivative rules:

19) f(x) = 3 · x - 8 → f'(x) = 3                                         Differentiation for the addition of two functions / Derivative of a power / Derivative of the product of a power and a constant / Derivative of a constant

23) f(x) = x² - 2 · x³ → f'(x) = 2 · x - 6 · x²                     Differentiation for the subtraction of two functions / Derivative of a power / Derivative of the product of a power and a constant

25) g(x) = √(9 - x) → g'(x) = - 1 / [2 ·√(9 - x)]                Differentiation of the square root / Chain rule

27) g(t) = 1 - 2 · t / 3 + 1 → g'(t) = - 2 / 3                       Differentiation for the addition of two functions / Derivative of a power / Derivative of the product of a power and a constant / Derivative of a constant

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Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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If P(A)= \(\frac{2}{3}\), P(B) = \(\frac{1}{4}\) and P(A and B)= \(\frac{2}{7}\), then the events A and B are dependent.

By comparing the probability of events A and B intersection (P(A and B)) to the product of their individual probabilities (P(A) * P(B)), we can find out whether the events are independent or dependent.

Condition of independent events,

If P(A) * P(B) = P(A and B)

Condition of dependent events,

If P(A) * P(B) ≠ P(A and B)

Given,

P(A) = \(\frac{2}{3}\)

P(B) = \(\frac{1}{4}\)

P(A and B) = \(\frac{2}{7}\)

Calculating P(A) * P(B) and compare it to P(A and B):

P(A) * P(B) = \(\frac{2}{3}\) * \(\frac{1}{4}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)

Since P(A and B) ≠ P(A) * P(B), therefore events A and B are dependent.

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The percentages of people taking the test who scores between 421 and 645 is: 68 %

The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

We are given:

Sample mean: x' = 553

standard deviation; s = 112

Thus:

x' - ns = 421

x' + ns = 645

Where n is the number of standard deviations from the mean. Thus:

553 - 112s = 421

112s = 553 - 421

112s = 132

s = 132/112

s ≈ 1

So 1 standard deviation from the means indicates a percentage of 68%

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Answer:

50

Step-by-step explanation:

The coefficient is amount of money in m (months)

The 50 is the amount of money

They are depositing $50 per month, 50m

Therefore, the coefficient is 50.

Answer:

50

Step-by-step explanation:

Answer:

The probability that one marble drawn at random is not blue is 70%

Answer:

7. 5

6. 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the numbers in the Venn diagram we get answers:

Answer:

I'm so confused

Step-by-step explanation:

did you forget to add a picture

1 ÷ 3 is the scale factor that takes parallelogram H to parallelogram I.

If Parallelogram I is a scaled replica of Parallelogram H, then perhaps the figure in which every length in the initial estimate is multiplied by the exact number.

Scale factor = size of new shape ÷ size of the old shape.

The magnification ratio of a parallelogram I is significantly 3 times that of parallelogram H this ratio could be only assumed when the data is not given.

The polygon will be reduced if the magnification ratio would be between 0 and 1. The picture will be magnified if the zoom ratio is larger than one.

The scale factor refers to the ratio of the old thing's scale to the new object's scale. Although the size of these ratios varies, they are useful.

Use negative magnification to enlarge the picture. Whenever the scale factor is negative, the value diverges from the scale.

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The complete question is -

Parallelogram I is a scaled copy of parallelogram H. What scale factor takes parallelogram H to parallelogram I in the image?

The scaling factor that transforms parallelogram H into parallelogram I is 1/3.

If Parallelogram I is a scaled-down version of Parallelogram H, then it might be the result of multiplying each length in the initial estimate by a precise value.

Scale factor is equal to new shape's size minus old shape's size.

A parallelogram I's magnification ratio is noticeably three times greater than a parallelogram H's. Only in cases where no data is provided may this ratio be assumed.

If the magnification ratio is in the range between 0 and 1, the polygon will be smaller. If the zoom ratio exceeds one, the image will be enlarged. The scale factor is the ratio of the scale of the old thing to the scale of the new thing.These ratios are helpful despite the fact that their sizes differ.

Enlarge the image by applying negative magnification. The value deviates from the scale whenever the scale factor is negative.

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An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

An inequality is comparison of  two values, showing if one is less than, greater than, or simply not equal to another value.

Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.

Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

Induction hypothesis:

Suppose 100n ≤ k³ for some positive integer k ≥ 10.

We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.

Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100

                                                 ≤ k³ + 3k²    (∵ k ≥ 10 )

                                                 ≤ k³ + 3k² + 3k

                                                 ≤ k³ + 3k²+3k + 1

So 100( k + 1 ) ≤ ( k + 1 )³, which is true.

Hence by the principle of mathematical induction, 100n ≤ k³ for every integer  k ≥ 10.

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Answer:

8

Step-by-step explanation:

The square of a number square rooted is the number itself.

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

Answer:

square, triangle, trapezoid,rectangle

The Two-dimensional figures are square, triangle, rectangle, and trapezoid.

Two-dimensional shapes do not have any thickness and can be measured on only two faces. These can be drawn on a sheet of paper with the constitution of two axises only.

The Two-dimensional figures that are cross-sections for each of the three-dimensional solids are:

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\(~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)\)

\(\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}\)

\(400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)\)

\(\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}\)

how much will it be in interest alone?

well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned

\(400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}\)